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Technical Notes Electronic Referencing Techniques for Quantitative NMR: Pitfalls and How To Avoid Them Using Amplitude-Corrected Referencing through Signal Injection Knut Mehr, Boban John, David Russell, and Daina Avizonis* Varian MR Systems, 3120 Hansen Way M/S D-298 Palo Alto California, California 94304 NMR spectroscopy can be a superior analytical technique for quantification of compounds dissolved in solution. Traditionally a chemical reference standard of known concentration is added to the sample. The concentration of the solute can then be determined by comparing the signal integrals. However, it can be inconvenient or impossible to use internal references. Electronic referencing was developed to circumvent problems with internal standards and has been used successfully in well-controlled situations. However, it is not always possible or convenient to have samples where the dielectric sample properties do not change from one to the next. We propose a modification of the old electronic referencing technique that takes into account the electronic changes between dissimilar samples. We have called this new technique Amplitudecorrected Referencing Through Signal Injection or ARTSI. NMR is a nondiscriminate linear detector. This means that if a solution of a compound is concentrated enough and has an NMR “active” nucleus such as 1H or 19F the spectrometer will detect it. The intensity integral of the resonance detected is directly proportional to its concentration in solution. Very few analytical techniques have such a clean and direct path to quantification. Today’s modern NMR spectrometers have improved in sensitivity, making quantitation practical, but they also have very stable transmitters and receivers that remove the necessity of requiring an internal standard of known concentration. This is especially important where it is impossible or inconvenient to add an internal concentration standard to the sample. One may measure a standard of known concentration and use that NMR spectrum to set integral values. These values may be transferred, with a few modifications, to another sample of unknown solute concentration and used to quantify the concentration of the unknown solute. One can imagine a few clever macros or software programs that a chemist could execute. However, even for an experienced * To whom correspondence
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spectroscopist this is an inconvenient and cumbersome solution. The fear is 2-fold. First, if the quantitation sample integral values are overwritten or lost then the calibration is lost and the chemist would need to return to the calibrant spectrum to retrieve and correct the integral values. The standard calibration integrals are in a spectrum or data set separate from the unknown’s data set. Second, the calibrant integrals may potentially be mis-set upon retrieval of the reference integral intensities. In the end having a peak, albeit an electronically synthetized reference peak, stored along with the unknown’s NMR data set leaves much less room for error and ambiguity. The calibrated internal synthetic reference signal represents a calibrated concentration that can be easily integrated and used. It is something that is easily used by all chemists, and because it is part of the free induction decay of the unknown sample’s data set, it cannot be easily lost or confused with other standard data sets. Approximately thirteen years ago, Serge Akoka patented an electronic referencing technique Electronic Referencing To access In vivo Concentrations” or ERETIC1 for imaging. This technique was later modified to work for high resolution spectrometers.2 The ERETIC technique has been used for a number of applications ranging from high-resolution NMR, solids NMR, to MRS imaging.3-6 For high-resolution NMR, a radio frequency signal at the observed frequency, typically proton, is electronically generated via a very low power shaped pulse on a decoupler or second channel. The signal is introduced directly into the probe on a spare channel, typically the X-channel, during acquisition. The X-channel is not necessarily tuned to the operating frequency. During acquisition, the proton coil may then detect the synthetic signal emanating, in theory, from the X-coil or channel. Since the ERETIC signal is detected on the same coil as the NMR signal, it has been assumed that it too experiences the changes in the (1) Barantin, L.; Akoka, S.; LePape, A., CNRS, F. P., Ed. France, 1995. (2) Akoka, S.; Barantin, L.; Trierweiler, M. Anal. Chem. 1999, 71, 2554–2557. (3) Burton, I. W.; Quilliam, M. A.; Walter, J. A. Anal. Chem. 2005, 77, 3123– 3131. (4) Dalvit, C. Prog. Nucl. Magn. Reson. Spectrosc. 2007, 51, 243–271. (5) Franconi, F.; Chapon, C.; Lemaire, L.; Lehmann, V.; Barantin, L.; Akoka, S. Magnetic Resonance Imaging 2002, 20, 587–592. (6) Ziarelli, F.; Caldarelli, S. Solid State Nucl. Magn. Reson. 2006, 29, 214– 218. 10.1021/ac800865c CCC: $40.75 2008 American Chemical Society Published on Web 10/10/2008
quality factor of the probe caused by the insertion of a sample into the detection coil.2 The ERETIC signal integral is calibrated against a reference standard sample. The same signal is then generated in the sample of unknown concentration and used as a concentration reference integral there by allowing the chemist to calculate the concentration of the unknown sample. Since this technique was adapted to high-resolution NMR, spectroscopists have encountered inconsistencies when applying it to a wider range of applications. Variations in quantitative performance appear to be associated with two different experimental aspects: probes and samples. From anecdotal evidence and our own experience, some probes behave more consistently than others. Likewise, samples that have dielectric properties very similar to or the same as the concentration reference standard do well with the ERETIC technique while those in different solvents or salt compositions can give large errors in quantitation. In short, it is important to recognize the limitations of a very useful technique. In this technical note, we explain and solve these shortcomings by taking advantage of stable and flexible instrumentation and using the basic reciprocity principle 7,8 to overcome the most serious limitations of earlier electronic referencing schemes. We call this new technique “Amplitude-corrected Referencing Through Signal Injection” or ARTSI. EXPERIMENTAL SECTION To challenge the quality factor of the NMR probe, a series of 2 mM sucrose, 0.24 mM 2,2-dimethyl-2-silapentane-5-sulfonic acid (DSS), and 0-250 mM sodium chloride solutions were prepared from a 200 mM sucrose and 24 mM DSS stock solution, and 2.5 M sodium chloride stock D2O solutions. The final volume of the samples was 700 µL in D2O. The NMR data were collected on a 600-MHz Varian NMR System (installed 2006) equipped a triple resonance probe (HCN) and VnmrJ Software (rev 2.2C). For each sucrose/DSS sample, the probe was tuned and matched followed by gradient shimming and a 90° pulse width calibration. The 90° pulse was manually calculated from 360° and 720° tip angle calibrations on the residual HOD and DSS signals. Each sample was inserted into the magnet, tuned, and calibrated at least six separate times. In general, the 90° pulses calculated from the 360° and the 720° pulse calibrations were within 0.1 µs of each other. This indicates a calibration accuracy of ∼1-3% for the given pulse power. Spectra with electronic referencing were collected using four scans, a calibrated 90° pulse for each sample, an acquisition time of 5 s, and interpulse delay of 25 s with a low-power presaturation of 5 s (35 s for each scan). Data were processed using a 0.5-Hz exponential line broadening and zero-filled to 524 288 data points. Integral resets were set according to Weiss.9 Data were acquired 10 times for each sample using both ERETIC and ARTSI techniques. The electronic reference signal injection required some minor system recabling as described by Akoka et al.2 or using an improved cabling scheme as shown in Figure 1. It was necessary to split the synthesizer input from the proton channel to the reference channel to maintain proper phase of the reference signal. The standard presaturation experiment was modified to generate (7) Hoult, D. I. Concepts in Magnetic Resonance 2000, 12, 173–187. (8) Hoult, D. I.; Richards, R. E. J. Magn. Reson. 1976, 24 (1969), 71–85. (9) Weiss, G. H.; Ferretti, J. A. J. Magn. Reson. 1983, 55 (1969), 397–407.
Figure 1. Schematic drawing of how one may recable a spectrometer so that the reference signal is coupled into the receive path between the probe and rf filter/preamplifier using a low-loss directional couplers. A splitter may be necessary for the synthesizer output from the observe channel to the reference generating channel to avoid reference signal phase changes. Abbreviations: TX, transmitter, RX, receiver, T/R, transmit/receive switch; CH1, spectrometer channel one, CH2, or CH3; spectrometer channel two or three, triangular symbols represent amplifiers.
the electronic reference signal during acquisition. The electronic reference signal was programmed as an exponentially decaying shaped pulse at the proton frequency using pbox.10 The shaped pulse was executed on the second or third channel (depending on how the system was cabled) during the acquisition time. The shaped pulse is automatically generated by the pulse sequence such that the operator can set acquisition time, offset, line width, phase, and intensity of the reference signal. The same pulse sequence was used for both ERETIC and ARTSI style data acquisition. In the “proof-of-concept” study presented here, 2 mM sucrose with 0.24 mM DSS in D2O was used as the concentration reference standard. The fine power used for the synthetic signal was adjusted until a reasonable integration value was achieved compared to the anomeric proton of sucrose. For the ARTSI technique, the reference signal power and reference sample’s 90° pulse width were also recorded (and maintained in the probe file). For the ARTSI technique, the intensity (fine power) of the electronic signal was adjusted based on the 90° pulse width of the sample in the magnet compared to that of the reference sample’s 90° pulse width as described Results and Discussion. RESULTS AND DISCUSSION In order to test how well the ERETIC technique works when the quality factor of the probe is changed by samples with increasing salt concentration, we acquired data using the ERETIC technique and analyzed it for six samples of 2 mM sucrose samples with sodium chloride concentrations ranging from no salt to levels above 250 mM. Each sample was carefully tuned, shimmed, and its 90° pulse calibrated. The data were analyzed according to Akoka et al.2 The results are summarized in Figure 2 and Table 1. As the salt concentration increases, the quality factor of the probe is decreased. From the data analyzed, it is clear that the ERETIC signal intensity did not accurately track (10) Varian, 2.2C ed.; Varian Inc.: Palo Alto, 2008 Varian NMR Software.
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must be scaled accordingly (see Supporting Information Figures 2 and 3). The reciprocity principle, introduced by Hoult and Richards in 1976 and subsequently reviewed in 2000,7,8 states that the signal strength is directly proportional to the square root of the quality factor of the probe. The quality factor is inversely proportional to the square of the 90° pulse width. Thus, in a given probe and sample, if the 90° pulse width is shorter then the quality factor of the probe is larger and vice versa. Since these relationships are straightforward, we can easily calculate the necessary power for the reference signal intensity based on the calibration sample’s pulse width and electronic reference signal power as follows: ERPWRsamp ) ERPWRcal(pw90cal/pw90samp)
Figure 2. Calculated concentration of 2 mM sucrose samples with increasing salt concentration results obtained using the ERETIC (filled in boxes) and ARTSI (filled in circles) techniques. Calculations were based on the anomeric signal compared to the reference signal placed at -1 ppm. Data for each sample were collected 10 times for each referencing technique. The error bars show the standard deviation of 10 measurements.
the changes in probe efficiency due to the changing dielectric properties of the samples in the probe. This is due to the fact that the intensity of the ERETIC signal, rather than being a function of only the inductive coupling between the coils and thus modulated only by the Q of the receive coil, is typically modulated by a variety of coupling factors. Those commonly include both inductive and capacitive coupling mechanisms between the tune/ match networks of both channels as well as between the NMR coils, but also by the return loss of the probe channel used to couple in the ERETIC signal. All these coupling factors combined are accurately described by the transmission factor, often referred to as isolation, between the observe port and the port used to couple in the ERETIC signal. While this transmission factor is also modulated as a function of changes in the observe coil Q and the associated tuning and matching changes, it is not normally modulated proportional to the intensity changes of the observe signal. As a general guideline, as soon as changes between samples require an adjustment of the tune and matching controls, the quantitative accuracy of the ERETIC method is being compromised. For these reasons, it is best not to inject a reference signal directly into the probe on any channel. The ARTSI technique, presented here, routes a reference signal through the full receive path of the spectrometer (Figure 1) using a directional coupler with very low insertion loss. This has the advantage that the path of the reference signal is well defined and controlled as well as it serves to test the electronics of the receive path for any degradation over time. The electronic reference signal intensity is adjusted the same as one would adjust it for the ERETIC technique except a reference pulse width and power are also recorded (see Supporting Information Figure 1 for example). Since each sample may change the receptivity of the probe coil and change the sensitivity of NMR signal received, the electronic signal intensity 8322
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where ERPWRsamp is the resulting power for the reference signal, ERPWRcal is the electronic reference signal power based on the calibration sample, pw90cal is the 90° pulse width of the tuned and matched calibration sample, and pw90samp is the 90° pulse width of the tuned and matched sample. The pulse power is assumed to be the same for both calibrant sample and unknown sample. The results for the ARTSI technique are shown in Figure 2 and Table 1. Clearly this technique successfully predicts the 2 mM concentration of sucrose in each of the samples measured to a much better degree than the data acquired using the ERETIC method. There is still some scatter in the data, which may be accounted for by various experimental errors, in particular how accurately the 90° pulse width of each sample was measured, variations in the NMR tubes, variations in volume measurements, and so forth. This scatter is no greater than that if one were to use the 0.24 mM DSS internal concentration standard (instead of the electronic reference) as shown in Table 1. A 5% variation or error in quantitative measurement is considered acceptable for most applications. It should be noted that the ARTSI technique can only be applied with accuracy when the probe can be tuned and matched to 50 Ω. If this requirement is not met, the reciprocity principle no longer applies and one cannot use the simple relationships described here. CONCLUSIONS We have shown that the ERETIC signal does not always accurately factor in changes in the receptivity of the proton coil with changing sample properties (see Supporting Information Figure 2). Instead, it reflects how the isolation between the reference port and observe port of the probe changes as a function of tuning and sample properties. The ERETIC technique can be applied where the tuning and matching between the reference sample and unknown samples does not change or in probes were the sample does not change the receptivity of the probe’s coil. This might be the case for probes that have very small sample volumes such as a room-temperature 1-mm probes or microcoil probes. The ARTSI technique does not send the reference signal through the NMR probe. It sends the electronic signal directly to the well-controlled receive path of the spectrometer and utilizes the well-established reciprocity principle (see Supporting Information Figure 3). The 90° pulse width of the sample is used as an inverse measure of the effective probe sensitivity change with differences in sample properties. The amplitude of the reference
Table 1. Comparison of Results for the ERETIC and ARTSI Techniques to the Internal 0.24 mM DSS Internal Standarda ARTSI technique
ERETIC technique
[NaCl] (mM)
[sucrose] (mM) based on DSS
[sucrose] (mM) based on ERb
anomeric signal to noise
[sucrose] (mM) based on DSS
[sucrose] (mM) based on ERb
anomeric signal to noise
90° pulse (µs)
0 50 100 150 200 250
2.00±0.04 2.04±0.03 2.04±0.04 2.04±0.06 2.03±0.05 2.03±0.03
2.00±0.04 2.06±0.03 2.04±0.04 2.05±0.06 2.07±0.04 2.09±0.03
306±10 293±12 258±09 253±12 247±09 237±06
2.00±0.04 1.98±0.04 2.02±0.03 2.00±0.04 2.02±0.02 2.03±0.04
2.00±0.04 1.89±0.04 1.81±0.03 1.63±0.04 1.84±0.04 1.73±0.04
319±09 291±10 258±09 255±10 245±06 245±09
6.43±0.07 7.03±0.08 7.50±0.14 7.96±0.06 8.16±0.07 8.59±0.09
a Standard deviations are shown for 10 measurements. The average calibrated 90° pulse witdths (for 6 independent measurements) and average signal to noise (10 measurements) are also shown. The anomeric proton of sucrose was used for signal to noise measurements with a 200 Hz noise region. Note, at 250mM the probe had reached the edge of its match window. This sample could not be matched as well as the others therefore the Principle of Reciprocity may no longer apply as can be seen as a loss of accuracy in the concentration measurement. This is a limitation of the probe used to gather the data and should not be interpreted to be a limit of the ARTSI technique. b ER, electronic reference.
signal is adjusted proportionally. We propose that the ARTSI technique can be used for a wide variety of samples and need not be limited to samples of very similar probe receptivity. The ARTSI technique takes into account changes in probe receptivity and corrects the reference signal intensity, which in turn gives a more accurate quantitation of the unknown sample’s concentration. We have presented only one way of solving the electronic referencing problem. Recently, Upton presented another solution where the reference signal is fully simulated and simply added to the digital NMR data.11,12 The intensity of this artificial signal is adjusted based on solvent, receiver gain, number of transients acquired, and other experimental factors are taken into account. While Upton presents a good general solution that can be used for a wide range of applications, it does require additional software, does not test the receiver path, and requires the accurate consideration of a wider range of parameters than required for ARTSI. The electronic referencing procedure introduced here as ARTSI is a simple improvement that can be easily implemented (11) Upton, R., SMASH, Chamonix, France, 2007. (12) Upton, R., ENC, Asilomar, California, March 10, 2008.
on any modern spectrometer without any additional software and minimal additional hardware. It can also be applied to a wide range of samples without recalibration. ACKNOWLEDGMENT We thank Phil Hornung, Christine Hofstetter, and Mark Dixon for their constructive input and technical advice, as well as Dimitris Argyropoulos and Peter Sandor for their pulse sequence writing expertise for this project. We also acknowledge the Varian Applications laboratory in Palo Alto for allowing the use of their spectrometers for this work. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.
Received for review April 29, 2008. Accepted September 4, 2008. AC800865C
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